A recent study of peanut allergies—the LEAP trial—explored the relationship between early exposure to peanuts and the subsequent development of an allergy to peanuts. Infants (4 to 11 months old) who had shown evidence of other kinds of allergies were randomly assigned to one of two groups. Group 1 consumed a baby-food form of peanut butter. Group 2 avoided peanut butter. At 5 years old, 10 of 307 children in the peanut-consumption group were allergic to peanuts, and 55 of 321 children in the peanut-avoidance group were allergic to peanuts.
We want test 0:1−2=0,:1−2≠0 where 1== the true proportion of children like the ones in this study who are exposed to peanut butter as infants that are allergic to peanuts at age 5 and 2== the true proportion of children like the ones in this study who are not exposed to peanut butter as infants that are allergic to peanuts at age 5 using =0.05.
The -value of this test is approximately 0. Because the -value of approximately 0 < = 0.05, we reject 0.
There is convincing evidence that the true proportion of children like the ones in this study who are exposed to peanut butter as infants that are allergic to peanuts at age 5 is different than the true proportion of children like the ones in this study who are not exposed to peanut butter as infants that are allergic to peanuts at age 5.
A 95% confidence interval for 1−2 is (−0.185,−0.093)(−0.185,−0.093).
Explain how the confidence interval provides more information than the test.
The confidence interval (INCLUDES / DOES NOT INCLUDE) 0 as a plausible value for p1–p2, which is consistent with the decision to (FAIL TO REJECT / REJECT) H0:p1–p2 = 0 . However, the confidence interval also tells us that any value between (0.185 / 0) and (0 / -0.93) is plausible for p1–p2 based on the sample data, and unlike the hypothesis test, the confidence interval gives us an estimate for p1–p2
